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Exercises 243
bill of $6000 for any day that a request is received. However, the
request will need to be made by 9.30 am.
At 9.00 am on 26 November outside temperatures are below
freezing. As a result, Central’s staff estimate that there is a 0.7
probability that the additional station will be required later in the
day if no request is made to the customer. If the customer is asked
to reduce usage it is virtually certain that the additional station will
not be required. Before making the decision on whether to send
the request to the customer Central has another option. It could
purchase a forecast from the local weather center at a cost of $1500.
For this payment the weather center will use a model to indicate
whether the additional station will be required. The accuracy of its
forecasts is shown by the following table of probabilities.
Weather center
forecast
Additional station
not required
Actual outcome
Additional station
required
Additional station 0.9 0.4
not required
Additional station 0.1 0.6
required
(a) (i) For the day in question, determine the expected value of the
imperfect information from the weather center and explain
your result.
(ii) Assuming that Central’s objective is to minimize expected
costs, advise them on the course of action they should take.
(b) Discuss the extent to which the expected monetary value (EMV)
criterion is likely to be appropriate to Central’s decision.
(11) A worker in a food plant has a rash on his left arm and the company
doctor is concerned that he may be suffering from Flaubert’s disease.
This can only occur as a result of biological contamination of the
raw materials that the worker handles in his job. However, the
disease is rare and has not occurred in the plant during the ten
years of its operation so the doctor estimates that the probability
that contamination exists in the plant to be only 2%, while there is
a 98% chance that the contamination is not present.
The doctor has now to advise the company’s board on whether
they should close the plant for two days to enable fumigation to
be carried out. This would certainly eradicate any contamination
but it would cost a total of $30 000. If the plant is not closed and